A NOVEL METHOD FOR RELATIVISTIC ENERGY OF A UNIT VECTOR FIELD IN LIE GROUPS VIA GALILEAN TRANSFORMATION

Abstract

In this paper, we firstly present a new approach for the computation of the energy of the moving particle in a Lie group R for a given reference system K. In this approach, we use geometrical descriptions of the curvature and torsion functions of the curve for the calculation. Then we consider a second reference system K*, which moves relative to K for an arbitrary direction with a uniform velocity under the Galilean transformation. Finally, we compute the relativistic energy of the moving particle considering relative reference system K*.